"The residents are listed at E.D. 295, 64, and 72."
Well I don't know how to translate E.D.'s into page numbers. But if you go to 1870 census to Vermont to Chittenden to Burlington it starts you at page 1 of 360. I didn't see E.D. listed anywhere on the page.
I did find a couple of people listed as "Sisters of Charity" on page 295, but much less than I would have expected for an Orphanage. I did find the "Home for Destitute Children" on page 125. Just incase anyone wants to see it. I didn't see anything for St. Joseph's on page 64 and wasn't going to search page by page. Apparently the institutions aren't indexed.